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Sensors and Actuators A 208 (2014) 37– 49

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Sensors and Actuators A: Physical

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Micromachined ultrasonic Doppler velocity sensor using nickel on

glass transducers

Minchul Shina, Zhengxin Zhaoa, Paul DeBitettob, Robert D. Whitea,∗

a Mechanical Engineering, Tufts University, 200 College Avenue, Medford, MA 02155, USAb Draper Laboratory, 555 Technology Square, Cambridge, MA 02139, USA

a r t i c l e i n f o

Article history:

Received 5 August 2013

Received in revised form 2 December 2013

Accepted 16 December 2013

Available online 3 January 2014

Keywords:

Micromachined

Ultrasound

Doppler

Velocity

Sensor

Array

a b s t r a c t

A micromachined array of 168 nickel-on-glass capacitive ultrasound transducers was used to demon-

strate a long range Doppler velocity measurement system. By using an electroplated nickel on glass

process, the total capacitance of the chip was reduced to 65 pF, resulting in a high signal to noise ratio

and allowing an operable range of 1.5 m. The range is limited by room reverberation level, rather than

electronic noise. The sensor array operates at a 180 kHz resonant frequency to achieve a half-angle −3 dB

beamwidth of 6◦ with a 1 cm2 die. The cMUT array was characterized using laser Doppler vibrometry

(LDV), beampattern measurements, range testing, and the ability to measure the velocity of a moving

plate. The sensor is capable of measuring the velocity of a moving reflector with a resolution of 6 cm/s,

at an update rate of 0.016 s, and with a range of 1.5 m (3 m round trip).

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Range finding and velocity measurement sensors are required

for a variety of navigation tasks including mobile robot navigation,

personal navigation systems, automotive sensing, micro air vehicle

navigation, obstacle detection, and map building [1–6]. A num-

ber of possible sensing modalities exist, including millimeter wave

RADAR systems, laser range finding systems, and infrared range

finding systems. Ultrasonic range finding and velocity measure-

ment is also an option with certain advantages.

Among suitable techniques, RADAR-based Doppler velocity or

distance measurement systems and laser rangefinders can provide

high accuracy. However, these systems suffer from high power con-

sumption and high cost. Laser rangefinders may also be sensitive to

ambient light conditions, and may not be able to penetrate heavy

rain or snow [7,8,27]. When compared with an ultrasonic array of

high enough frequency (e.g. 180 kHz as described here), millimeter

wave RADAR tends to require a larger aperture to provide a narrow

beam, resulting in a physically large system. For instance, a modern

automotive millimeter wave RADAR system operating at f = 77 GHz

∗ Corresponding author. Tel.: +1 617 627 2210.

E-mail address: [email protected] (R.D. White).

[27] with a desired half-angle beamwidth of � = 6◦, would require

an aperture of L ≈ 3.7 cm [32, p. 192],

L ≈ c/f

sin �(1)

Eq. (1) is valid for acoustic and RF waves. Hence, due to the much

lower speed of sound as compared to RF, the same beamwidth can

be achieved at 180 kHz, as done in the ultrasonic device described

here, with a 1 cm aperture. Another approach for obstacle detection

in mobile robotics is infrared reflectance sensors. These devices

tend to be low cost and low power consumption. However, the

infrared rangefinder tends to have low accuracy, and may suffer

from ambient light sensitivity and sensitivity to surface character-

istics [8,9].

Ultrasonic sensors are another alternative for navigation and

obstacle detection. They have advantages of low cost, small size,

low power consumption, and simple signal processing [10]. Ultra-

sound will scatter and absorb in a different manner than lasers

and IR, if for no other reason than the difference in wavelength

(millimeters vs. hundreds of nanometers or a few microns). In

addition, it will scatter and absorb differently than millimeter

RADAR, despite the similar wavelength, due to the different wave

modality (acoustic rather than electromagnetic). Thus, due to

their low cost, size, and power, as well as the additional envi-

ronmental information they provide, ultrasonic sensors are an

0924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.sna.2013.12.025


38 M. Shin et al. / Sensors and Actuators A 208 (2014) 37– 49

attractive sensor technology to include in a mix of navigational

sensors. It is, however, important to note that ultrasonic sen-

sors also can suffer from the drawback of multipath reflections,

which can result in poor distance measurements, and may also

be sensitive to changes in reflecting surfaces and ambient condi-

tions.

Ultrasonic distance measurement systems are available com-

mercially, although they typically operate at frequencies near

40 kHz. Some examples include the well-known Polaroid ranging

module that uses a time of flight distance measurement method

and operates at frequencies between 49 and 60 kHz [24]. Another

example is the SRF series ultrasonic sensor from Devantech [Devan-

tech, Norfolk, England] which is smaller than the Polaroid system,

with a 4.3 cm × 2 cm front aperture. This system operates at 40 kHz.

For a 1 cm aperture transducer, the size used for the device

described in this paper, a frequency of 40–60 kHz results in a half-

angle beamwidth of 35–60◦, according to Eq. (1). Hence the sensors

are not very directional, contributing to problems with reverbera-

tion and multipath reflections.

It is, however, expected that a more directional sensor will gen-

erate, and pick up, fewer multipath echoes. Through the use of

MEMS technology, the operating frequency can be increased to

180 kHz, as demonstrated here, and thus the half-angle beamwidth

can be reduced from 35–60◦ to 6◦, resulting in substantially

improved directionality. The increase in frequency reduces the

range of the sensor to some degree due to the increase in bulk

absorption at higher frequencies, but the range can still be kept

acceptably high.

MEMS based ultrasonic sensor systems including both piezo-

electric micromachined ultrasound transducers (pMUTs) and

capacitive micromachined ultrasound transducers (cMUTs) have

been described for other applications previously [e.g. 16, 22,

25, 26, 29, 31, 33, 35], with a preponderance of applications in

biomedical ultrasound and non-destructive testing. A few authors

[10,11,38,40] have described MEMS-based ultrasonic distance

measurement systems. These systems use either piezoelectric or

thermal actuation principles, and achieve a range of 10 cm to, at

most, 1.3 m.

Indeed, although MEMS-based rangefinders have the advan-

tage of low cost and high portability with a small size, they must

overcome challenges in terms of power output and sensitivity that

can result in a limited range [11]. For example, a previous system,

described by the authors, which used polysilicon surface microma-

chined cMUTs only achieved a 30 cm (60 cm round trip) range [38].

To overcome the short-range problem, the cMUT device described

here was developed with a low stray capacitance and a high drive

voltage drive. This combination allowed an achievable range to the

reflector of 1.5 m (3 m round trip).

The device described in this paper is fabricated in a 3 layer

nickel-on-glass MEMS fabrication process for cMUT sensors that

was critical for achieving low stray capacitance. The low capac-

itance is achieved due to the complete lack of a conducting or

semiconducting substrate below the signal traces and bond pads;

by using a dielectric (glass) substrate, stray capacitance between

traces and bond pads is dramatically reduced when compared to

a device built on a semiconducting substrate with a thin layer

dielectric. This process has some similarities to LIGA and LIGA-like

processing [12–15] but is considerably simpler to implement. The

process enables fabrication for the production of a range of low

stray capacitance sensors; for instance we have used this process

for shear sensors [21]. This paper outlines the methods for creat-

ing a solution for a smaller, lower cost, low capacitance, long range,

and low power MEMS ultrasonic array for velocity measurement in

air. This is the only example in the literature of a cMUT based ultra-

sonic velocity measurement system in air with a range of more than

30 cm.

2. Design and modeling

The transducer array consists of 168 individual array elements

arranged in a 14 × 12 hexagonal grid on a 1 cm2 chip. The transmit

area of the array is 9 mm × 9 mm. The 1 cm size of the chip, which

sets the array aperture, was selected to give the same beamwidth

as typical automotive millimeter wave RADAR systems (6◦) at an

achievable operating frequency (180 kHz) [27]. Aperture and oper-

ating frequency can be modified to change beamwidth according to

Eq. (1), within constraints of system size and achievable resonant

frequency.

The individual elements are 600 �m diameter, 9 �m thick

Nickel, separated from a 390 �m diameter Cr/Au bottom electrode

by a 5 �m air gap. Element diameter was selected to be signifi-

cantly less than the wavelength of sound at the 180 kHz operating

frequency (at 180 kHz, � = 1.9 mm), but to be as large as possi-

ble (which maximizes signal) without collapsing due to in-process

adhesion related failure (e.g. stiction). The elements were packed

as closely together as possible in order to maximize signal. Due to

the geometry of a hexagonal close packed array, adjacent rows are

spaced 0.72 mm center-to-center, and adjacent columns are spaced

0.63 mm center-to-center. Since the element motion is larger near

the center than the edge, the center of the electrode contributes

more signal than the outside of the electrode. However, both center

and edge contribute the same amount of stray capacitance. Thus, it

is beneficial to use an electrode that is somewhat smaller than the

diaphragm, in order to improve sensitivity. The exact size was not

optimized. Twenty-eight 10 �m diameter vent holes are included

in each diaphragm for release etching and static pressure equal-

ization. The vent holes also control the damping. All elements are

connected in parallel. The geometry is shown in Fig. 1.

A fully coupled electro-acoustic-mechanical model was con-

structed for the system. The model is similar to that described

previously for other MEMS cMUTs [16,38]. The model includes

the diaphragm stiffness and mass, including residual stress effects,

squeeze film damping, backing cavity compliance, vent hole damp-

ing, and external air impedance. The acoustic-mechanical model is

coupled in a bi-directional fashion to the electrical domain via elec-

trostatic coupling. Fig. 2 shows the geometry and an equivalent

acoustic circuit for the model.

The model derivation begins from the equation for a thin bend-

ing plate with residual stress, forced by distributed pressures from

the electrostatics and the air,

D∇4u(r, t) − T∇2u(r, t) + �Nih∂2u(r, t)

∂t2

= 1

2V2(t)

ε0

(g0 − u(r, t))2˚(a2 − r) + p1(t) − p2(t) (2)

where r is the radial coordinate, t is time, u(r,t) is the displacement

of the diaphragm, positive downwards, V(t) is the applied voltage,

p1(t) and p2(t) are the pressures above and below the diaphragm, ε0

is the permittivity of free space, g0 is the gap height (5 �m), �Ni is the

density of Nickel, taken to be 8900 kg/m3 [17], and h is the thickness

of the diaphragm (9 �m). It is assumed that the pressure in the

gap and the pressure in the external acoustic medium are nearly

constant with radial position, since for the frequencies of interest,

near 180 kHz, the wavelength of sound, � = 1.9 mm, is greater than

the radius of the diaphragm, a1 = 0.3 mm. The electrostatic force

only acts over the area of the electrode, which is a circle of radius

a2. Thus the Heaviside step function ˚(a2− r) appears on the right.

D and T are the bending stiffness and tension, respectively,

D = Eh3

12(1 − �2)(3)

T = �Rh (4)


M. Shin et al. / Sensors and Actuators A 208 (2014) 37– 49 39

Fig. 1. Transducer geometry. Top left: full array chip. Top right: individual element, top view. Bottom: individual element, cross-section.

Fig. 2. Electro-acoustic-mechanical model of a single axisymmetric element.

Table 1Geometric properties of the nickel-on-glass cMUT sensor.

Symbol Property Value Units

a1 Radius of diaphragm 300 �m

a2 Radius of bottom electrode 195 �m

h Thickness of nickel layer 9 �m

g0 Thickness of sacrificial layer (air gap) 5 �m

r1 Radius of diaphragm vent holes 5 �m

N Number of vent holes in diaphragm 28 Dimensionless

where E and � are the elastic modulus and Poisson ratio of the elec-

troplated Nickel, taken to be 205 GPa and 0.31 [18,19] and �R is

the residual stress in the Nickel film. The residual stress for plated

nickel thin films prepared from nickel sulfamate plating baths can

vary considerably, from at least −80 MPa to +80 MPa, depending on

additives, plating temperature, current density, and film thickness

[e.g. 36]. Summaries of the geometric and material properties for

the model appear in Tables 1 and 2.

Steady state harmonic solutions with time variation ejωt are

sought. For receive operation, the bias is held constant, V(t) = Vdc.

Table 2Material properties of the diaphragm.

Symbol Property Value Units Reference(s)

�Ni Density of nickel 8900 kg/m3 [17]

E Modulus of elasticity of nickel 205 GPa [18]

�R Residual stress of nickel −80 to 80 MPa [36]

� Poisson’s ratio of nickel 0.31 Dimensionless [19]



For transmit operation the applied voltage is harmonic at ωac,

V(t) = Vaccos(ωact). In transmit mode, this will produce a primary

steady state response at ω = 2ωac due to the square law electro-

statics. A Galerkin procedure can be employed to determine u(r)

[42–44]. A functional form is assumed that satisfies the boundary

conditions with an unknown coefficient or coefficients:

u(r) = U0 (r) (5)

where U0, in this case, is the unknown centerpoint displacement.

After substitution of Eq. (5) for u(r) in Eq. (2), multiplication of both

sides of Eq. (2) by u(r), and integration over the domain, a result is

arrived at for U0,

U0 =[

D

∫ a1

0 (r)∇4 (r)rdr∫ a1

0 (r)rdr

− T

∫ a1

0 (r)∇2 (r)rdr∫ a1

0 (r)rdr

− h�Niω2

∫ a1

0 2(r)rdr∫ a1

0 (r)rdr

− ε0

g30

(V2

dc +V2

ac

2

) ∫ a2

0 2(r)rdr∫ a1

0 (r)rdr

]−1

·(∫ a2

0 (r)rdr∫ a1

0 (r)rdr

ε0

4g20

V2ac + (p1 − p2)

)(6)

This result can be used to determine the structural acoustic

impedance in Fig. 2, where the volume velocity of the diaphragm

is driven by the differential pressure and the effective electrostatic

pressure:

Q = 1

Zst

(∫ a2

0 (r)rdr∫ a1

0 (r)rdr

ε0

4g20

V2ac + (p1 − p2)

)(7)

where Q is the oscillatory volume velocity of the diaphragm,

Q = 2�jω

∫ a1

0

u(r)rdr (8)

Thus Q can be related to the centerpoint displacement by

U0 =Q

2�jω∫ a1

0 (r)rdr

(9)

Then, from Eqs. (6) and (7), the structural impedance can be

determined,

Zst = h�Ni

∫ a1

0 2(r)rdr

2�(∫ a1

0 (r)rdr

)2jω +

[D

∫ a1

0 (r)∇4 (r)rdr

2�(∫ a1

0 (r)rdr

)2− T

∫ a1

0 (r)∇2 (r)rdr

2�(∫ a1

0 (r)rdr

)2−

ε0

∫ a2

0 2(r)rdr

g30

2�(∫ a1

0 (r)rdr

)2

(V2

dc +V2

ac

2

)]1

jω(10)

The impedance shows a mass in series with a stiffness, as

expected. The negative stiffness of the electrostatic spring is evi-

dent in the last term. The result will only be valid up through the

first resonant frequency, above which the assumed modeshape will

no longer be valid. The structural impedance can be written as

Zst = Mstjω + 1

Cst jω+ 1

Celjω(11)

where Cst is the structural compliance for the first mode, Cel is the

effective linearized electrostatic spring compliance, and Mst is the

structural mass for the first mode. From (10) and (11) it is seen that

Mst = h�Ni

∫ a1

0 2(r)rdr

2�(∫ a1

0 (r)rdr

)2(12)

Cst =[

D

∫ a1

0 (r)∇4 (r)rdr

2�(∫ a1

0 (r)rdr

)2− T

∫ a1

0 (r)∇2 (r)rdr

2�(∫ a1

0 (r)rdr

)2

]−1

(13)

Cel = −[

ε0

∫ a2

0 2(r)rdr

g30

2�(∫ a1

0 (r)rdr

)2

(V2

dc +V2

ac

2

)]−1

(14)

In order to compute the structural impedance and the electro-

static coupling, a deflection shape, �(r), must be selected. Results

will be shown below for a few different possible choices of shape.

The integrals can be performed analytically or numerically.

The pressures above and below the diaphragm, p1 and p2, are

computed from the acoustic circuit in Fig. 2. The acoustic capac-

itance represents the compressibility of the air in the gap [23],

Cac =g0�a2

1

�0c2(15)

For flow in a thin gap below an oscillating perforated plate, the

flow resistance including squeeze film damping and viscous flow

resistance through the holes can be approximated as [30],

Rac = 12

�g30

NC(A) + 8

�r41

N

(h + 3�r1

8

)(16)

The first term comes from “squeeze film” resistance to flow in

the gap behind the diaphragm. The second term represents the

resistance to flow through the holes in the diaphragm. r1 is the

radius of the vent holes, N is the number of holes in the diaphragm,

and is the viscosity of air, taken to be 1.85 × 10−5 Pa s. The param-

eter C(A) is

C(A) = A

2− 3

8− A2

8− 1

2ln(√

A) (17)

where A = Nr21

/a21

is the ratio of the hole area to the full diaphragm

area. The result is identical to Skvor’s formula [39].

The complex acoustic pressure on the top surface of the

diaphragm comes from a combination of any incoming pressure

wave and the pressure generated by the oscillating element acting

as an acoustic source. The net velocity that creates the acoustic

source is the difference between the velocity through the holes

and the velocity of the diaphragm itself, as indicated by the topol-

ogy of the acoustic circuit. The pressure on the top surface of the

diaphragm is therefore

p1 = Zenv · (Qhole − Q ) + 2P0 (18)

The term P0 represents an incoming acoustic plane wave. This

is included to model an external acoustic input coming from the

environment in “receive” mode. The factor of 2 comes from the

scattered rigid wave. In transmit mode, P0 = 0.

The environmental impedance can be estimated from the radi-

ation impedance of a clamped circular diaphragm oscillating in the

static bending modeshape. The environmental impedance has been

derived by Greenspan [28],

Zenv ≈ �0c

a21

(1

2�(ka1)2 + 0.296j(ka1)

)(19)

c is the speed of sound, taken to be 343 m/s, and �0 is the equilib-

rium density of the acoustic medium, taken to be 1.21 kg/m3. This



Fig. 3. Comparison between the measured center point vibratory response for the transmit (TX) and receive (RX) chips, and the predictions from the model. (a) Shows

the magnitude results for four different possible choices of shape function and with zero residual stress. (b) Shows the comparison using the best fit values of structural

impedance given in Table 3.

is a good approximation for ka1 < 0.5. At low frequencies this is an

acoustic mass in parallel with an acoustic radiation resistance. An

extensive discussion of the computation of the radiation impedance

of circular diaphragms including multiple possible modeshapes

and extending to higher frequencies can be found in Lax [34], Porter

[37], and Greenspan [28]. For this device there is not much to be

gained by more complicated environmental impedance models.

The environmental impedance has little impact on device dynam-

ics. This would not, however, be the case for a water loaded device,

where environmental impedance would have a much more signif-

icant impact.

All the impedances in the acoustic circuit have been defined.

Using elementary circuit theory, the volume velocities Q and Qhole

can be computed in terms of the external driving pressure P0 in

receive mode, or the AC drive voltage Vac in transmit mode. Once Q

and Qhole are known, the magnitude of the oscillatory centerpoint

deflection can be computed from Eq. (9).

A direct comparison of model predictions can be made to the

diaphragm center point oscillation measured using a laser Doppler

velocimetry (LDV) system. In this experiment, the diaphragm is

driven by an AC voltage of amplitude Vac with an applied DC bias,

resulting in an electrostatic force at the same frequency as the

AC drive. For this type of excitation, the driving V2ac in the volt-

age source should be replaced with 4 VdcVac. Otherwise the model

is unchanged. In Fig. 3, the predicted center point displacement

from the dynamic model is compared to the measured center point

response for an element on each of the two chips. The data is nor-

malized to the product of the applied DC bias of 9 V and the applied

AC peak drive of 1 V.

In Fig. 3(a) model predictions are shown for the following pos-

sible shape functions, with an assumed residual stress of zero. The

measured LDV response of the two chips is also shown. All choices

of shape produce predictions of center frequency and peak response

that are within a factor of 2 of the measured result, but with the

unknown residual stress and lack of certainty about the best choice

of shape function, uncertainties remain in model predictions prior

to performing dynamic experiments. The shapes used in Fig. 3(a)

are: the response of an axisymmetric circular bending plate with a

clamped edge to a uniform static pressure load [41, p. 178],

(r) =(

1 −(

r

a1

)2)2

(20)

the response of an axisymmetric circular bending plate with a sim-

ply supported edge to a uniform static pressure load [41, p. 168],

(r) = 1 − 23 + �

5 + �

(r

a1

)2

+ 1 + �

5 + �

(r

a1

)4

(21)

the first in vacuo vibratory mode of a circular tensioned membrane

[32],

(r) = J0

(2.4048

r

a1

)(22)

and the first in vacuo vibratory mode of a circular plate with

clamped edges [34],

(r) = 0.0528I0

(3.196

r

a1

)+ 0.9472J0

(3.196

r

a1

)(23)

Due to uncertainties in the nickel residual stress and boundary

conditions, it is unclear which of these choices will give the most

accurate result. For low stress (pure bending) at low frequencies,

Eq. (20) or Eq. (21), should work well, depending on the flexibility

of the anchors, and therefore the best choice of boundary condi-

tion. For high stress (tension dominated) near resonance, Eq. (22)

is expected to be a good choice. For low stress (bending dominated)

near resonance, Eq. (23) may produce superior results. Any of these

shapes can be used to predict an approximate frequency response

curve, as shown in Fig. 3(a). This is very useful for targeting the

design to approximately achieve a desire center frequency, gain,

and bandwidth. By testing multiple shapes we also achieve a sense

of expected levels of variation due to changes in residual stress and

boundary conditions. Typically, we find that exactly matching the

model to the dynamic response of the system can only be done

after fitting at least one parameter using experimental data. It is

then possible to iterate on the design using the fitted parameter to

achieve a closer match to a target operating point. Alternatively, one

could solve Eq. (2) numerically at a series of frequencies. This will

require selection of boundary conditions and estimation of resid-

ual stress, as well as estimation of the relative magnitude of the

pressure and electrostatic driving terms on the right hand side. The

resulting solutions could be used as a frequency dependent (r),

resulting in frequency dependent structural impedances. However,

due to uncertainties in the residual stress and boundary conditions,

and variation in film properties from wafer to wafer or chip to chip,

these impedances will still not exactly match experimental results.



Table 3Structural impedance of the diaphragm as computed from Eqs. (12) and (13) with

�R = 0 MPa with (r) = J0(2.4048 r/a1), and compared to the best fit values for fitting

the LDV data in Fig.3.

Analytical result,

�R = 0,

(r) = J0(2.4048·r/a1)

Best fit RX Best fit TX

Cst 3.4 × 10−18 m3/Pa 3.8 × 10−18 m3/Pa 3.8 × 10−18 m3/Pa

Mst 4.1 × 105 kg/m4 2.6 × 105 kg/m4 2.2 × 105 kg/m4

Once dynamic data is available, the best option for predicting

the acoustic response is to determine the structural compliance and

mass, Cst and Mst, by fitting the measured response for each chip.

The model is still physics based, but the structural uncertainties

have been removed by fitting to data. Fig. 3(b) shows a comparison

to the data with these best fit values. The best fit values of Cst and Mst

are given in Table 3, and compared for interest to the results using

the first in vacuo tensioned membrane mode of Eq. (22) with zero

residual stress. For subsequent computations, the best fit values of

Cst and Mst will be used.

The farfield transmitted pressure from the array can be com-

puted at any point in the field (rf, �f, �f) by summing the

contribution from each element in the array treated individually

as a directional source,

P(rf , �f , �f ) = j�0ω

2�·

N∑m=1

1

Rm· (Qhole − Q )e(−˛c−jk)Rm H(�f ) (24)

where Qhole− Q is the net source volume velocity: the difference

between the diaphragm volume velocity and the flow through the

vent holes. Rm is the scalar distance from the center of the mth array

element to the field point. H(�f) is the directivity of an individual

element. The acoustic absorption is ˛c in Np/m. At frequencies near

180 kHz in air of this is well modeled using the classical absorption

coefficient [32],

˛c = ω2

2�0c3

(4

3+ � − 1

Pr

)=(

1.37 × 10−11 Np · s2

m

)f 2 (25)

where � = 1.40 is the ratio of specific heats for air near 20 ◦C, and

Pr = 0.75 is the Prandtl number of air near 20 ◦C. f is the frequency

in Hz.

At the drive frequency of 180 kHz, ka1 is close to unity, so the

individual elements are somewhat directional. The beampattern

of a baffled piston is used to approximate the beampattern of the

individual elements,

H(�f ) = 2J1(kaeff sin �f )

kaeff sin �f(26)

where � is the angle, measured from the normal to the field point,

and J1 is the Bessel function of the first kind, order 1. For the

purposes of directivity calculation, the effective radius, aeff, of the

transmitting element should be used. Since the element deforms as

a circular bending plate, the effective radius of an equivalent baf-

fled piston is somewhat less than the physical radius. An effective

radius equal to 70% of the physical radius is a good approxima-

tion. This was determined by a comparing Eq. (26) to a numerical

computation of the farfield beampattern for a baffled circular plate

oscillating in the clamped static shape given in Eq. (20).

The summation is over the 168 array elements. Since all the

elements are identical, all the Qhole− Q are the same, and only the

distance to the field point, Rm, changes. It should be noted that this

dynamic model neglects any acoustic coupling between the ele-

ments via mutual radiation impedances or through the connected

backing cavities. Computations (not shown) were done including

mutual radiation impedances as described in Porter [37]. This had

little impact on the computed beampattern, due to the relatively

low impedance of the air. Note that mutual radiation impedance

would be much more important if operating in a heavy fluid such

as water.

3. Fabrication

The cMUT sensor was fabricated with an electroplated nickel

surface micromachining process. The process started with a

550 �m thick soda lime glass wafer as shown in Fig. 4 panel

1. To clean the wafer, a Piranha clean was conducted for 5 min.

75 nm/225 nm thick Cr/Au interconnects (a bottom electrode and

Fig. 4. Fabrication process using nickel and copper electroplating.



Fig. 5. Photograph of the entire nickel cMUT array after packaging (left) and a corner of the array at higher magnification (right).

bonding pads) were deposited with sputtering and patterned by

liftoff using liftoff resist (LOR) as shown in Fig. 4 panels 2 and 3. Sub-

sequently, a thin seed layer of Ti/Cu (30 nm/300 nm) was deposited

in preparation for copper plating and patterned by liftoff using LOR

as shown in panel 4. 8 �m thick AZ 9245 photoresist was then spun

on as a mask for the plated Cu sacrificial layer, seen in panel 5. Before

copper plating, the copper oxide was removed by a short dip in the

Cu plating solution with no current applied. As shown in panel 6, a

5 �m sacrificial layer of copper was then electroplated to cover the

entire substrate except anchor regions and contact pads in a com-

mercial copper plating solution [Technic, Inc., Cranston, RI]. The

plating solution was 5–10% copper sulfate, 15–20% sulfuric acid,

with chloride ions and brightener additives. Plating was conducted

at room temperature, a bath pH of 0.5, and a plating current den-

sity of approximately 5 mA/cm2. The plating rate was 150 nm/min.

After copper plating, the sacrificial layer was complete.

An AZ 9260 photoresist mold was then deposited and photo-

patterned. This photoresist mold defines the structural layer

including the holes, as shown in panel 7. The 9 �m thick struc-

tural layer was electroplated at 50 ◦C in a commercial nickel

sulfamate plating solution [Technic Inc., Cranston, RI], consist-

ing of 20–35% nickel sulfamate, 0.5–1.5% nickel bromide, and

1–3% boric acid, with a pH of 4.0. The plating rate was approx-

imately 100 nm/min and the resulting surface roughness Ra was

approximately 30–40 nm. To minimize the surface roughness of the

plated structure in both plating procedures, a small plating current

(≈5 mA/cm2) was used, as well as agitation and filtration of the

plating solution. After nickel plating, a protective photoresist layer

was spun on for dicing the wafer. Finally, the resist was stripped

and the sacrificial layer was etched away in a mixture of 1 part

Acetic Acid to 1 part 30% Hydrogen Peroxide to 18 parts DI water

for 24 h, producing the structure seen in panel 8. The chip was then

rinsed in water, isopropanol, and methanol, and finally allowed to

air dry in a dry box at low relative humidity.

The chip was packaged into a 16 pin DIP package using epoxy

and ball bonded with 25 �m diameter gold wire. Fig. 5 shows

photographs of the finished device. Tables 1 and 2 give the tar-

get geometric and the material properties of the sensor structure.

There is some deviation from the target structural layer thickness

in the fabricated devices. For the transmit (TX) chip and receive

(RX) chips, the measured thickness of the structural nickel was

9.5 �m ± 0.5 �m and 8.5 �m ± 0.5 �m respectively. For both chips,

the thickness of the air gap was within 0.5 �m of the target thick-

ness of 5.0 �m.

4. Electronics

The nickel-on-glass chip has a high predicted snapdown voltage

of 360 V. The high snapdown voltage of the nickel-on-glass chip

is due to the thick structure and the air gap. The high snapdown

device can sustain a high input voltage swing on the transmitter,

and a high DC bias voltage on the receiver to increase output and

sensitivity if desired.

Fig. 6. Transmit bridge amplifier circuit with the cMUT chip.

Modified from [20].



Fig. 7. Receive electronics.

In order to produce a higher voltage swing for the input, a

bridge amplifier stage was used for the transmitter. A high voltage

operational amplifier (OPA 445 high voltage FET-Input operational

amplifier [Texas Instrument, Dallas, TX]) was used to increase the

voltage swing across the cMUT to as much as 180 Vpeak-to-peak while

operating from ±45 V supplies. In operation, 140 Vpeak-to-peak was

used at 180 kHz due to slew rate limitations on the amplifiers. Fig. 6

shows the circuit. The drive is configured as a bridge amplifier,

allowing voltage swings twice as large as the power supply range

through a differential drive scheme.

The receive electronics, shown in Fig. 7, consist of a DC bias

source, a voltage preamplifier, and subsequent gain stages. The DC

bias of 10 V was provided using the ADR01 voltage reference IC

[Analog Devices, Wilmington, MA]. In receive mode, the element

acts as a current source through electrostatic coupling. With the DC

bias held fixed across the element, the oscillatory current delivered

to the electrical side by a single element is

I =∫ a2

0 (r)rdr∫ a1

0 (r)rdr

ε0Vdc

g20

Q (27)

The voltage preamplifier integrates this current using the self-

capacitance of the MEMS device, Csensor, of 65 pF. The preamplifier

is realized using the AD797 low noise operational amplifier [Ana-

log Devices, Wilmington, MA]. A 100 k� DC stabilizing resistor,

R9, is included between the voltage amplifier input and ground,

resulting in a high pass filter with a cutoff frequency of 25 kHz.

Following the preamplifier, the signal is passed into a series of

three operational amplifier based circuits, each configured with

a bandwidth of 2–800 kHz and 26 dB of voltage gain. Within the

passband of the system, between 25 kHz and 800 kHz, the voltage

output at the end of the chain is simply

Vout = GN2

Csensor jωI (28)

where G = 8000 is the voltage gain of the amplifier chain, N2 = 168 is

the number of cMUTs in the array, Csensor = 65 pF is the capacitance

of the chip, and I is the current delivered by an individual element,

taken from Eq. (27).

Fig. 8 shows the physically realized receive electronics. The

board consists of a ZIF socket for holding the packaged cMUT chip,

the circuit above, and power and signal connectors. The electronics

are enclosed by a grounded metal box for protection from electro-

magnetic interference (EMI). An optional 90 V DC bias source is also

included, although due to thermal problems the higher DC bias was

not used.

Using the model with the best fit structural impedance values

of Table 3, and the electronics as described here, the transmitted

pressure and receive sensitivity for these two chips can be com-

puted. The results are shown in Fig. 9. The on-axis sound pressure

level at 1 m from the transmit array is 69 dB SPL, when driving with

140 Vpp at 180 kHz (14 Vpp at the input to the bridge amplifier).

Fig. 8. Physical realization of the receive electronics.



(a) (b)

20

40

60

80

30

210

60

240

90

270

120

300

150

330

180 0100 15 0 20 0 25 00

0.5

1

1.5

Sen

s (V

/Pa)

Frequ ency Response, Rece ive Sensitivity

100 15 0 20 0 25 0-15 0

-10 0

-50

0

50

100

Frequ ency (kHz)

Ph

ase

(deg

)

Fig. 9. Predicted array performance using the best fit structural impedance from Table 3. (a) Predicted farfield transmit beampattern at 180 kHz for the transmit array at

a distance 1 m from the center of the array. Results are for 140 Vpp drive, and are presented in dB SPL (dB re 20 �Parms). (b) Predicted receive array sensitivity. Results are

reported at the end of the amplifier chain (output of U3 in Fig. 7) with 10 Vdc bias and for a normally incident plane wave.

This requires ±35 V supplies for the bridge amplifier circuit. Note

that 180 kHz is not exactly matched to the transmit array peak, so

higher outputs could be generated if driving exactly at the chip

peak frequency. The predicted −3 dB beamwidth for this calcula-

tion is 11.4◦ (5.7◦ on either side of center). The peak sensitivity for

the receive array for a normally incident plane wave with a 10 Vdc

bias applied is 1.38 V/Pa at 170 kHz. The predicted receive array

response at 180 kHz is 1.14 V/Pa.

5. Experimental results

The driven frequency responses of all 168 elements in the

transmit and receive arrays were measured using LDV, producing

frequency response plots similar to that seen in Fig. 3. For the

receiver chip, the average value of the resonant frequency of 168

elements is 158.56 kHz and the standard deviation is 4.96 kHz, with

166/168 yield. For the transmitter chip, the average value of the

resonant frequency of 168 elements is 188.40 kHz and the standard

deviation is 10.06 kHz with 163/168 element yield. For highest

performance, element yield should be high, and the resonant

frequencies should all be well matched. As shown experimentally,

the achieved yield and matching is sufficient for long-range

operation. However, improving yield and tightening tolerances on

the resonant frequency would result in improved performance.

A free field measurement was conducted using the pair of cMUT

chips. The transmitter produced a continuous wave acoustic signal

at 180 kHz. The receive array was 10 cm away and always ori-

ented directly toward the transmit array. The transmit array was

rotated in place using a micrometer rotation stage. The RMS receive

response at the drive frequency was recorded at each angle. Fig. 10

shows a comparison between the measured and modeled beam-

pattern for the pair. The agreement is very good, showing a −3 dB

half beamwidth of approximately 6◦ as predicted by the model. The

first sidelobes are down approximately −15 dB as expected.

In operation, there is the need for electromagnetic interference

(EMI) protection to prevent RF communication between the trans-

mit and receive electronics. In order to accomplish this, the cMUT

array chips and electronics are mounted in grounded metal boxes

with shielded signal lines, as shown in Fig. 11.

To investigate the achievable range of the system, range test-

ing was conducted using continuous wave acoustics at 180 kHz, as

shown in Fig. 12. The drive signal was 14 Vpp to the bridge amplifier

at 90 kHz, resulting in acoustics at 180 kHz due to the square law

electrostatics. The DC bias on the receiver side was 10 V. The nickel-

on-glass chip has their angle fixed during range testing. Three

reflector materials were used: plywood, aluminum, and acrylic. The

reflector was oriented orthogonal to the transmit/receive main axis.

Experimental results show a maximum range of 1.5 m as shown

Fig. 13. Received signal power decreases with distance according

to the expected law including geometric spreading and acoustic

absorption [32],

EL = SL50 cm − (7 dB/m)(2D − 50 cm) − 6 dB log2(D/50 cm)

(29)

-40

-20

30

210

60

240

90

270

120

300

150

330

180 0

Fig. 10. Comparison between the modeled (solid line) and measured (open cir-

cles) beampattern for the transmit/receive array in a free field test. Normalized to

maximum pressure (0 dB at peak).



Fig. 11. Photograph of the transmit/receive system including shielding boxes.

where EL is the received echo level in dB, SL50 cm is the source level

at 50 cm, taken from the measured data. 7 dB/m is the single direc-

tion acoustic absorption in air at 180 kHz, and 6 dB is the geometric

spreading per doubling of distance between the source and reflec-

tor. Note that this is 6 dB rather than 3 dB since there is a two

directional travel. D is the distance between the source/receiver

and the reflector.

With D ≥ 1.5 m, the signal decreases below the background

reverberation level (−67 dB Vrms). Each material has the simi-

lar range results. The noisefloor in the diagram is the electronic

noisefloor. Noise level is always dependent on sampling. In this

experiment, the sampling frequency was Fs = 1 MHz and the num-

ber of samples was 220, resulting in a total data acquisition time of

1.0 s per point.

Finally, a computer controlled velocity sled was used to demon-

strate measurable Doppler shifts, as shown in Fig. 14. Control of

the sled velocity was accomplished using a DC motor and optical

shaft encoder. Continuous acoustic waves were again generated by

a stationary transmit array at 180 kHz, reflected off of the moving

aluminum plate at various velocities, and received by the stationary

receive array. The distance to the reflector varies during the test.

At its closest approach the reflector is 3 cm from the sensors. At

its most distant, the reflector is 1 m away. For velocity comparison,

a laser fiber optic velocimeter was used, also reflecting off of the

moving plate.

The Doppler shift for a stationary transmitter/receiver and mov-

ing reflector, at speeds well below the speed of sound, is [32]

�f = fc2vc

(30)

where fc = 180 kHz is the carrier frequency, v is the velocity of the

reflector relative to the transmit/receive arrays, and c is the speed

of sound. A positive Doppler shift indicates motion of the reflec-

tor toward the transducers, and a negative Doppler shift indicates

motion away.

Fig. 15 shows spectrograms of the received ultrasonic signal

for various motions of the reflector. Data was captured at 1 MHz,

with the total number of sampling points N = 220, corresponding to

approximately 1 s of data. The spectrogram uses a 214 point Ham-

ming window with 50% overlap. This is a time window of 0.016 s,

thus the minimum resolvable shift in frequency is �f = 61 Hz which

corresponds to a velocity resolution of 5.8 cm/s. The spectrograms

are presented with the frequency shift noted on the left axis, and

the corresponding velocity v from Eq. (30) on the right axis.

The white dashed line in each plot shows the velocity as mea-

sured by LDV. In the LDV data, there are missing points and drop

outs due to poor reflection at some times. The Doppler measure-

ment of velocity from the cMUT does not exhibit this problem. The

velocity profile measured by the cMUT Doppler matches the LDV

data very well. The velocity command sent to the motor controller

is noted in each panel of the figure, although it is clear from both

the cMUT and LDV data that there is considerable true variation of

the plate velocity around the setpoint, including vibrations of the

plate.

Fig. 12. Diagram and photograph of the range measurement test set up.



0 50 10 0 15 0 20 0-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

Distance to Reflec tor (cm)

Rec

eive

Res

po

nse

(dB

V)

Aluminu mPlywoo dAcryli c

Noise floo r=300 μV/rtHz

Reve rberation Leve l=480 μVrms

@ 180 kHz

Equ ation 29

Fig. 13. Range test result using cMUT array with three reflection materials such as aluminum, plywood, and acrylic.

Fig. 15(a) shows a rapid motion of the plate toward the arrays.

Considerable vibration and velocity variation of the plate are

observed. These are real motions of the plate and are accurately

captured by both the ultrasonic and LDV systems. An excellent

match is obtained between the two measurement methods. It is

clear from the figure also that the received response becomes

louder as the reflector approaches, as expected. Fig. 15(b) shows

a case of the reflector moving toward the sensor at a low speed.

In this panel, the resolution of velocity due to the finite time

window is evident. When using a 16 ms time window, as was

done here, the frequency resolution in the FFT is equivalent to a

5.8 cm/s velocity resolution. Fig. 15(c) shows a case of the reflec-

tor moving away from the sensor at an intermediate speed. In the

spectrogram, there are ‘ghost’ bands at harmonics of the shifted

frequency. These were most noticeable in data where the reflec-

tor was moving away from the arrays. This phenomenon is likely

caused by multiple reflections between the transmit/receive arrays

and the reflector. Fig. 15(d) is an example of an intermediate speed

movement toward the sensors with many similarities to panel

(a).

Fig. 14. Diagram and photograph of the test set up used for measuring Doppler velocity response of the system.



Fig. 15. Spectrograms of the received ultrasound signal presented as a Doppler shift away from the carrier frequency of 180 kHz. The corresponding velocity computed from

Eq. (30) is given on the right axis. The dashed white line shows the velocity measured by the laser velocimeter.

6. Conclusion

An ultrasonic velocity sensor using MEMS technology is

explored as a navigational sensor. The system works off of a differ-

ent sensing modality than other rangefinding sensors such as laser,

RF RADAR, or infrared rangefinders. The nickel-on-glass chip was

fabricated with a low cost 3 layer nickel-on-glass surface micro-

machining process. The process is simple to apply with no high

performance material layers that must be carefully tuned. A com-

putational model has been developed that predicts many of the

features of the system response, including excellent models of

absolute system output, damping, bandwidth, and array beampat-

tern.

The system operates at 180 kHz in a continuous wave modal-

ity. Beampattern measurements show a 12◦ −3 dB beamwidth (6◦

either side of center). The sidelobes are 15 dB below the main lobe.

These results agree with theoretical models. The beamwidth of

the system is considerably narrower than most other ultrasonic

rangefinders on the market, which may reduce problems with mul-

tipath reflections. This claim needs further verification.

A velocity sled was constructed and used to demonstrate mea-

surable Doppler shifts at varying velocities. The Doppler shifts

match very well with laser velocimetry measurements of a moving

aluminum plate at velocities up to 0.5 m/s. The velocity resolution

is approximately 6 cm/s in a 60 Hz band (60 velocity updates per

second). Velocity resolution and time resolution can be traded off

dynamically. By using a longer time window and thereby reduc-

ing temporal resolution, velocity resolution can be increased. This

tradeoff can be managed flexibly during signal processing.

Future work on this system will consider frequency modulated

operation for distance measurement, and characterization with

acoustic reflectors that may be relevant for navigation problems.

The system will be further miniaturized and integrated with a

robotic platform for demonstration as an alternative navigational

sensor.

Acknowledgement

This work was funded by the Draper Labs University Research

and Development Program.

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